2. Re: Financial Maths for ct1

What's that angled bracket on top of n? In my copy of "Higher Algebra" by Hall & Knight,(1955 Ed; 1st Edition 1887) there is something similar but the angled bracket appears on the lower left - this was the old notation for n!

3. Re: Financial Maths for ct1

oh sorry I should've explained it, the LHS= the present value of a level increasing annuity payable continuously for n years at a rate of i percent p/a

4. Re: Financial Maths for ct1

Originally Posted by BenHowe
$\noindent Well here's some hints to at least evaluate that sum in your question. Once you evaluate the integral, you should see that you effectively need to compute a sum of the form$

$S = \sum_{k=1}^{n}k v^{k-1}.$

$\noindent There are a few ways to evaluate such a sum. Here's a hint for one method. I'll assume v \neq 1 (if v = 1, the series is just an arithmetic series).$

\noindent Multiply both sides by v, so vS = \sum_{k =1}^{n} kv^{k}. Now see what you get if you consider S -vS (hint: align like powers of v). You should end up with something familiar that will let you solve for S. Hope this helps!

5. Re: Financial Maths for ct1

I think I must be doing something wrong. For the summation I just want

$\sum_{t=1}^{n}te^{-\delta t} \\ \text{However I get} \sum_{t=1}^{n} -\frac{t}{\delta}e^{-\delta t}[1-e^{\delta}]$

6. Re: Financial Maths for ct1

Originally Posted by BenHowe
oh sorry I should've explained it, the LHS= the present value of a level increasing annuity payable continuously for n years at a rate of i percent p/a
Oh yea. I should have remembered that notation.

7. Re: Financial Maths for ct1

Oh yeah sorry I skipped stuff as well $v=e^{-\delta}$, where v is (1+i)^-1, so discounting whatever for 1 period but delta is the force or the rate of interest payable continously. so v=(1+i)^-1=e^-delta

8. Re: Financial Maths for ct1

Thanks for the help guys I realised my errors and can do it/understand it now. Thanks heaps! I'd upload the solution but I don't know how to put the actuarial angle in the bos LaTeX editor only on the LaTeX editor on my computer. That and you guys would find it very boring

9. Re: Financial Maths for ct1

Hey,

I think the answer is yes but I can't clearly explain why. Help please Capture.PNG

10. Re: Financial Maths for ct1

Dw all good standard integral properties

11. Re: Financial Maths for ct1

this all looks cancerous, do we ever have to do stuff like this in applied finance or is this just actuarial work?

12. Re: Financial Maths for ct1

No this is financial maths for actuaries. In saying that, you will encounter some of it like interest rates compounded continuously or momently etc. I just think the treatment of the material is a little different. I'll let you know though

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